A coupling of moving morphable void and component approach for the topology optimization of hydrogel structures involving recoverable large deformation is proposed in this paper. In this approach, the geometric parameters of moving morphable voids and components are set as design variables to respectively describe the outline and material distribution of hydrogel structures for the first time. To facilitate the numerical simulation of large deformation behavior of hydrogel structures during the optimization process, the design variables are mapped to the density field of the design domain and the density field is then used to interpolate the strain energy density function of the element. Furthermore, the adjoint sensitivity of the optimization formulation is derived and combined with the gradient-based algorithm to solve the topology optimization problem effectively. Finally, two representative numerical examples of the optimization of isotropic hydrogel structures are used to prove the effectiveness of the proposed method, and the optimization design of an anisotropic bionic hydrogel structure is presented to illustrate the applicability of the method. Experimental results are also presented to demonstrate that the explicit topologies obtained from the method can be directly used in the manufacture of hydrogel-based soft devices.

A micromechanics-based ductile fracture initiation theory is developed and applied for high-throughput assessment of ductile failure in plane stress. A key concept is that of inhomogeneous yielding such that microscopic failure occurs in bands with the driving force being a combination of band-resolved normal and shear tractions. The new criterion is similar to the phenomenological Mohr–Coulomb model, but the sensitivity of fracture initiation to the third stress invariant constitutes an emergent outcome of the formulation. Salient features of a fracture locus in plane stress are parametrically analyzed. In particular, it is shown that a finite shear ductility cannot be rationalized based on an isotropic theory that proceeds from first principles. Thus, the isotropic formulation is supplemented with an anisotropic model accounting for void rotation and shape change to complete the prediction of a fracture locus and compare with experiments. A wide body of experimental data from the literature is explored, and a simple procedure for calibrating the theory is outlined. Comparisons with experiments are discussed in some detail.

Tests have been carried out on thin closed-ended tubes of alpha brass subjected to various combinations of torque and internal pressure. The effect of loading, unloading, and reloading along different loading paths has been investigated, including the effect on the shape of the yield surface, and the form of the curve of representative stress and representative strain. The behavior of the material for initial loading suggests that the material is isotropic in the plane of the surface of the tube but is anisotropic in a radial direction. A form of yield criterion and representative stress which correlates these results has been deduced, but the results of the tests for the second loadings of the specimens cannot be correlated in terms of a nested set of similar yield surfaces. The evidence for or against the existence of corners or pointed vertices on the yield surface is inconclusive.

Stress-strain relations are given for an initially isotropic material, which is macroscopically homogeneous, but inhomogeneous on a microscopic scale. An element of volume is considered to be composed of various portions, which can be represented by subelements showing secondary creep and isotropic work-hardening in plastic deformation. If the condition is imposed that all subelements of an element of volume are subjected to the same total strain, it is demonstrated that the inelastic stress-strain relations of the material show anisotropic strain-hardening, creep recovery, and primary and secondary creep due to the nonuniform energy dissipation in deformation of the sub-elements. Only quasi-static deformations under isothermal conditions are considered. The theory is restricted to small total strains.

The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

Mechanical properties of porous materials depend on their micro-architectural characteristics. Freeze casting is an effective method to fabricate micro-architectured porous scaffolds. Three key characteristics generated during freeze casting are wall thickness, number of domains at the cross section, and transverse bridges connecting adjacent walls. To specifically study the effect of these structural characteristics on the mechanics and anisotropic compressive properties of scaffolds, we utilize additive manufacturing, i.e., 3D printing, to fabricate strictly designed cubic scaffolds with varying one characteristic at a time. We then compare strength, toughness, resilience, stiffness, and strain to failure in three orthogonal directions of the scaffolds, including longitudinal and transverse directions. To compare these multidimensional mechanics in a single diagram, we use a previously developed radar chart method to evaluate different scaffolds and unravel the effect of the structural characteristics. We find that the multidimensional mechanics can be effectively tuned by the micro-architectural characteristics. Notably, the buckling resistance of the scaffolds depends on all three structural characteristics. Our results show that an increased number of domains leads to enhanced toughness in all three directions. Increasing wall thickness leads to enhanced mechanical properties but comes at the price of losing small-sized pores, which is not favored for certain applications. In addition, adding transverse bridges increases not only the transverse strength of the scaffolds but also the longitudinal strength as they also enhance the buckling resistance. Our study provides important insights into the structure–property relationships of 3D-printed micro-architectured porous scaffolds.

The plasticity of a polycrystalline aggregate is expressed in terms of the plasticity of the individual grains. It is assumed that the local deviation of stress from the average stress is proportional to the local deviation of strain from the average strain, and it is assumed that plastic flow begins when there is an average of three active slip systems per grain. The plastic states of a grain are mapped as a function of the orientation of the crystallographic axes. A coexistence of different states of strain with different rotations of the axes at the same state of stress can be correlated with the occurrence of deformation bands. A range of orientations is illustrated in which the axes tend to congregate quickly and then move more slowly toward a stable end orientation. The residual strain which would be observed by x-ray diffraction after the release of stress is calculated for three sets of diffracting planes. The applications of the theory have so far been limited to face-centered cubic polycrystals with intrinsic elastic isotropy.

A theoretical and experimental program involving methods of calculating creep in rotating disks at elevated temperatures is described. This program consisted primarily of the following: ( a ) Obtaining forged disks from the same ingot of 12 per cent chrome steel, all disks being forged and heat-treated in the same manner; ( b ) making spin tests at 1000 F on three of these disks for periods up to about 1000 hr; ( ) making long-time tension-creep tests at 1000 F on many specimens cut out circumferentially from several of the other disks at stresses approximating those of the spin tests; ( d ) investigating theoretical methods of calculation of creep deformation in such disks; and ( e ) comparison of spin-test results with those calculated theoretically using average tension-creep data. It was found that available methods of calculating rotating disks based on the Mises criterion gave creep deformations too low compared to the test values, i.e., on the unsafe side for design. Considerably better agreement between test and theoretical results is obtained if the latter is based on the maximum-shear theory. Some discussion is given of the reasons for the better agreement obtained using the latter theory; these are believed to be related in part to the anisotropy of the forged material tested. Further tests on other materials are necessary before general conclusions can be drawn; however, in the absence of test data it is suggested that a conservative course in design for such disks is to apply the maximum-shear theory.

This investigation deals with a study of the plastic behavior of anisotropic metals. By extending Hill’s theory of plastic flow of anisotropic metals, plastic stress-strain relations for anisotropic materials with strain hardening are developed. Applications of these relations are also made to plane-stress and plane-strain problems with anisotropy. The effect of anisotropy on the stress distribution and on the pressure to produce yielding in a thick-walled cylinder under internal pressure is discussed. The influence of anisotropy on the interpretation of conventional biaxial tension-tension and tension-torsion tests is also considered in this study.

The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

The authors assess a plastic stress-strain law of anisotropic strain-hardening type which they previously developed on the basis of explicit consideration of the polycrystalline nature of metals and the mechanism of plastic deformation. The assumptions made are reviewed, together with the successes and limitations of the theory. The authors indicate the lines along which they feel that improvement of the theory is to be sought.

The elasticity of a polycrystalline aggregate is expressed in terms of the elasticity of the individual grains. The stress within each grain is estimated with the aid of an analysis of the stress distribution around a spherical cavity in an isotropic medium. The strain within each grain is expressed in terms of the average stress in the polycrystal as a whole by pseudoelastic constants which are related to the actual elastic constants. The calculated elasticities for physical tests and for x-ray diffraction measurements in polycrystals are given for a few cubic metals.

A loading function is a relation between combined stresses for which the beginning of plastic flow takes place. The loading function for a given material is different depending upon the initial plastic strains produced. That is, the initial stress or strain history influences the subsequent loading function. This paper gives the results of an experimental investigation to determine the validity of certain loading functions proposed for anisotropic materials. The study reported was conducted for an aluminum alloy 24S-T and the state of stress covered was biaxial tension. These stresses were produced in the usual way by subjecting thin-walled tubular specimens to axial tension and internal pressure. The test results showed that none of the existing loading functions is adequate for interpreting the plastic stress-strain relations obtained. Tests also were made to determine the change in the loading function with increase in plastic flow. It was found that the loading function did not remain symmetrical with respect to the original function, nor was the new loading function the same as the original except for a shift of origin. However, the test results support in a qualitative way the concept of the so-called “yield corner.”

Combined tension and torsion experiments for six tubular 24S-T4 aluminum-alloy specimens with considerable initial anisotropy are reported. In all cases the results reveal the existence of corners on the yield loci of the material.

Variations of thickness, anisotropy, and asymmetry of loading usually tend to increase the mathematical difficulty of obtaining solutions to the small-deflection problems of plate bending. However, for the bending of a cylindrically aeolotropic disk twisted about its diameter and having a certain thickness variation, it is possible to obtain a relatively simple solution in closed form. This solution is presented here, numerical results being given for oak and for isotropic material.